Budding transition for bilayer fluid vesicles with area-difference elasticity (original) (raw)
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Budding transitions of fluid-bilayer vesicles: the effect of area-difference elasticity
Physical Review E, 1994
Budding and vesiculation are prominent shape transformations of fluid lipid-bilayer vesicles. We discuss these transitions within the context of a curvature model which contains two types of bending energy. In addition to the usual local curvature elasticity~, we include the effect of a relative areal stretching of the two monolayers. This area-difFerence elasticity leads to an effective nonlocal curvature energy characterized by another parameter K We argue that the two contributions to the curvature energy are typically comparable in magnitude.
Scaling analysis of narrow necks in curvature models of fluid lipid-bilayer vesicles
Physical Review E, 1994
Under appropriate conditions fiuid lipid-bilayer vesicles in aqueous solution take the form of two (or more) compact shapes connected by a narrow neck (or necks). We study the limit {termed "vesiculation") in which the neck radius a approaches zero. On the basis of elastic equations, derived originally by Deuling and Helfrich [J. Phys. (Paris) 37, 1335 (1976)] for a bending-energy model (the spontaneouscurvature model), we show analytically that, at vesiculation, the local curvatures of the two regions joined by the neck satisfy a simple, universal "kissing" (osculation) condition. Furthermore, for points near but not at the vesiculation limit, a is small but nonzero and there is characteristic scaling behavior. For example, in the surface tension {0) and pressure (p) variables, the vesiculation boundary is a line in the (o,p) plane, and the quantity a lna scales linearly with the distance (Lcr, hp) from the boundary. These relations have been observed numerically, but no analytic discussion has previously appeared in the literature. Results for the spontaneous-curvature model generalize easily to other (more physical) bending-energy models.
The Effect of Variable Spontaneous Curvature on Dynamic Evolution of Two-Phase Vesicle
Journal of Advanced Chemical Engineering, 2017
This article aims to study the effect of non-uniform distribution of spontaneous curvature on shape transformation of two-phase vesicles via an evolutionary method. Their dynamic evolution is developed based on conventional Helfrich theory, considering bending of the membrane and friction in the surrounding fluid in each phase with variable spontaneous curvature. The variation of spontaneous curvature is assumed to be a function of arc length in each domain considering the effects of inducing factors (surrounding solution concentration and the membrane-protein interactions such as scaffolding and insertion). Membrane pearling from a large vesicle is simulated by the model and compared with the result of constant curvature and also with empirical observations. It can be shown that accurate simulation of some membrane deformation mechanisms depends on careful consideration of key factors such as the SC variations. In addition, the importance of different uniform and non-uniform distributions of spontaneous curvature is discussed with reference to specific cases.
Equilibrium budding and vesiculation in the curvature model of fluid lipid vesicles
Physical Review A, 1991
According to a model introduced by Helfrich [Z. Naturforsch. 28c, 693 {1973)],the shape of a closed lipid vesicle is determined by minimization of the total bending energy at fixed surface area and enclosed volume. We show that, in the appropriate regime, this model predicts both budding (the eruption of a satellite connected to the parent volume via a neck) and vesiculation (the special case when the neck radius goes to zero). Vesiculation occurs when the minimum is located at a boundary in the space of configurations. Successive vesiculations produce multiplets, in which the minimum-energy configuration consists of several bodies coexisting through infinitesimal necks. We study the sequence of shapes and shape transitions followed by a spherical vesicle of radius Rz, large on the scale Ro set by the spontaneous curvature, as its area A increases at constant volume V =4+R&/3. Such a vesicle periodically sheds excess area into a set of smaller spheres with radii comparable to Ro. We map out this (shape) phase diagram at large volume. In this region the phase diagram is dominated by multiplets and reAects the details of the shedding process. The overall effect of successive vesiculations is to reduce the energy from a quantity of order R v down to zero or near zero when the area reaches 3 V/Ro, however, the decrease is not uniform and the energy E (A, V) is not convex. 'I'he physical origin of the spontaneous curvature under given experimental conditions is a matter of present interest and even controversy. Nonzero values of co may arise, for example, from chemical asymmetry between the interior and exterior of the membrane' or from different areas of the two leaves of the bilayer (the bilayer-couple mechanism). " Whether these mechanisms suffice to explain observed shapes is unclear. In any case, we must keep in mind that the "constant" co may depend on both microscopic (chemical) and macroscopic (geometrical) variables. In what follows, we shall study a model system in which co is taken to be constant. If under laboratory conditions co turns out to depend on the surface area A 43 6843
arXiv: Soft Condensed Matter, 2019
We investigate the mechanics of heterogeneous vesicles having a collection of phase-separated domains with different preferred curvatures. We develop approaches to study at the coarse-grained level and continuum level the role of phase separation, elastic mechanics, and vesicle geometry. We investigate the elastic responses of vesicles both from passive shape fluctuations and from active deformations. We develop spectral analysis methods for analyzing passive shape fluctuations and further probe the mechanics through active deformations compressing heterogeneous vesicles between two flat plates or subjecting vesicles to insertion into slit-like channels. We find significant domain rearrangements can arise in heterogeneous vesicles in response to deformations. Relative to homogeneous vesicles, we find that heterogeneous vesicles can exhibit smaller resisting forces to compression and larger insertion times into channels. We introduce quantitative approaches for characterizing heterog...
Physical Review E, 1995
The equilibrium shapes of fluid-phase phospholipid vesicles in an aqueous solution are controlled by bending elasticity. The regime of nonvesiculated shapes at reduced volume v) 1/v 2 involves the interplay of Bve branches of distinct stationary shapes: pears, prolates, oblates, stomatocytes, plus a branch of nonaxisymmetric shapes with the symmetry D2&. We exploit a method for calculating explicitly the stability of arbitrary axisymmetric shapes to map out in a numerically exact way both the stable phases and the metastability of the low-lying shape branches. To obtain additional required information about nonaxisymmetric shapes, we calculate these by numerical minimization of the curvature energy on a triangulated surface. Combining these two methods allows us to construct the full (shape) phase diagram and the full stability diagram in this region. We provide explicit results for values of the bending constants appropriate to stearoyl-oleoyl-phosphatidylcholine; generalization to other values is straightforward.
Dynamic shape transformations of fluid vesicles
Soft Matter, 2010
We incorporate a volume-control algorithm into a recently developed one-particle-thick mesoscopic fluid membrane model to study vesicle shape transformation under osmotic conditions. Each coarsegrained particle in the model represents a cluster of lipid molecules and the inter-particle interaction potential effectively captures the dual character of fluid membranes as elastic shells with out-of-plane bending rigidity and 2D viscous fluids with in-plane viscosity. The osmotic pressure across the membrane is accounted for by an external potential, where the instantaneous volume of the vesicles is calculated via a local triangulation algorithm. Through coarse-grained molecular dynamics simulations, we mapped out a phase diagram of the equilibrium vesicle shapes in the space of spontaneous curvature and reduced vesicle volume. The produced equilibrium vesicle shapes agree strikingly well with previous experimental data. We further found that the vesicle shape transformation pathways depend on the volume change rate of the vesicle, which manifests the role of dynamic relaxation of internal stresses in vesicle shape transformations. Besides providing an efficient numerical tool for the study of membrane deformations, our simulations shed light on eliciting desired cellular functions via experimental control of membrane configurations.
Spontaneous curvature of fluid vesicles induced by trans-bilayer sugar asymmetry
European Biophysics Journal, 1999
We present measurements of the effective spontaneous curvature of fluid lipid bilayers as a function of trans-bilayer asymmetry. Experiments are performed on micrometer-scale vesicles in sugar solutions with varying species across the membrane. There are two effects leading to a preferred curvature of such a vesicle. The spontaneous curvatures of the two monolayers as well as their area difference combine into an effective spontaneous curvature of the membrane. Our technique for measuring this parameter allows us to use vesicle morphology as a probe for general membrane-solute interactions affecting elasticity.
Shape instabilities in vesicles: A phase-field model
The European Physical Journal Special Topics, 2007
A phase field model for dealing with shape instabilities in fluid membrane vesicles is presented. This model takes into account the Canham-Helfrich bending energy with spontaneous curvature. A dynamic equation for the phase-field is also derived. With this model it is possible to see the vesicle shape deformation dynamically, when some external agent instabilizes the membrane, for instance, inducing an inhomogeneous spontaneous curvature. The numerical scheme used is detailed and some stationary shapes are shown together with a shape diagram for vesicles of spherical topology and no spontaneous curvature, in agreement with known results.
The European Physical Journal E, 2010
We have studied the relaxation dynamics of shape fluctuations in unilamellar lipid vesicles by neutron spin echo (NSE). The presence of a hybrid curvature-compression mode coexisting with the usual bending one has been revealed in the experimental relaxation functions at high q. Differently to the conventional relaxation ∼ q 3 typical for bending modes, the hybrid mode was found to relax as ∼ q 2 , which is compatible with a dissipation mechanism arising from intermonolayer friction. Complementary data obtained from flickering spectroscopy (FS) in giant unilamellar vesicles confirm the existence of both modes coexisting together. By combining NSE and FS data we have depicted the experimental bimodal dispersion diagram, which is found compatible with theoretical predictions for reliable values of the material parameters. From the present data two conventional dynamical methods (NSE and FS) have been shown to be suitable for measuring intermonolayer friction coefficients in bilayer vesicles.